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Integral expressions for the numerical evaluation of product form expressions over irregular multidimensional integer state spaces

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Title Integral expressions for the numerical evaluation of product form expressions over irregular multidimensional integer state spaces
 
Creator MANJUNATH, D
SIKDAR, B
 
Subject normalizing constants
queuing-networks
queueing networks
normalising constant
 
Description Ill this paper we consider stochastic systems defined over irregular, multidimensional, integer spaces that have a product form steady state distribution. Examples of such systems include closed and BCMP type of queueing networks, polymerization and genetic models where the system state is a vector of integers, n = [n(1),...,n(M)] and the steady state solution is Of the form pi(n) = Pi i = 1 (M) f(i) (n(i)). To obtain useful statistics from such product form solutions, pi(n) has to be summed over some subset of the space over which it is defined. We consider situations when these subsets are defined by a set of equalities and inequalities with integer coefficients. as is most often the case and provide integral expressions to obtain these sums. Typically, a brute force technique to obtain the sum is computationally very expensive and algorithmic solutions covering specific forms of f(i)((i)) and shapes of the space over which these are known. In this paper we derive general integral expressions for arbitrary state spaces and f(i)(n(i)). The expressions that we derive here become especially useful if the generating functions f(t)(n(t)) call be expressed as a ratio of polynomials in which case, exact closed form expressions can be obtained for the sums. The integral expressions that we derive here have wide applications and we demonstrate them by three examples in which we model finite highway cellular systems, copy networks in multicast packet switches and BCMP queueing networks.
 
Publisher SOC COMPUTER SIMULATION
 
Date 2011-10-27T07:49:35Z
2011-12-15T09:12:19Z
2011-10-27T07:49:35Z
2011-12-15T09:12:19Z
1999
 
Type Proceedings Paper
 
Identifier PROCEEDINGS OF 1999 SYMPOSIUM ON PERFORMANCE EVALUATION OF COMPUTER AND TELECOMMUNICATION SYSTEMS,326-333
1-56555-174-5
http://dspace.library.iitb.ac.in/xmlui/handle/10054/16226
http://hdl.handle.net/100/2599
 
Source Symposium on Performance Evaluations of Computer and Telecommunications Systems (SPECTS 99),CHICAGO, IL,JUL 11-15, 1999
 
Language English